I see the cross flat bars setting on the ribs of bed floor as 'potential' problem. Obviously, but not mentioned, spacers needed under bars where bolts go thru as they are between ribs.
One is even with the foam, some weight will be concentrated. Softening the edges would help but any flexing of bed or bars will be at bar edges and top of ribs.
Which if doesn't lead to scissoring the sheet metal may at minimum wear thru coatings to see some corrosion. Which leads to second concern, aluminum bolted to steel.
I honestly cant see enough sideways force to warrant tying to frame, or cause bed to yield using a simpler method but not my truck. You'll need to do what your comfortable with.
That said, If it were mine and it seems main concern is how close doors get to jack feet, I'd look at removable jack feet.